Question

Particle track detectors are used to measure the speed of particles
if the lifetime of the particle is known. Particle X has a lifetime
of 256.2 ps. These particles are created in an experiment inside
the detector by a given reaction. The particles leave 10.6 cm long
tracks on average before they decay into other particles not
observable by the detector.
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What is the average speed of the particles in terms of the speed of
light?
Hints:
The speed of the particle is the ratio of the track length and the
lifetime. However the simple ratio of these two quantities gives
unphysically high speed: 1.379 c. The reason is that the length of
the track is measured in the resting frame of the detector. On the
other hand the lifetime of the particle is its life expectancy
measured in the frame moving with the particle. Either transform
the length of the track to the particle's frame, or the particle's
lifetime to the detector's frame. You can take the ratio of the
tracklength and the lifetime only if they are from the same
reference frame.